The magneto-optic effect, also known as the Faraday effect, was first described by Michael Faraday in 1845 and occurs in most optically transparent dielectric materials, including liquids, when they are subject to strong magnetic fields. The magneto-optic effect, manifested as an induced optical activity, is able to rotate the plane of polarization of an input optical beam that propagates parallel to the direction of the magnetic field in the material. The strength of the magneto-optic effect is given by the formula:θ=BVl  (1)where theta is the angle of rotation; B is the magnetic field; V is the Verdet constant for the material and l is the effective length of material contained within the magnetic field. Unlike the electro-optic effect, the magneto-optic effect causes a true rotation of the plane of polarization for any input polarization angle. In a simple electro-optic device, only pure rotations of 90° are available; all other intermediate voltages produce different degrees of elliptical polarization states from a linear input state, but a Faraday rotator will truly rotate the plane of input polarization through any angle, so long as a sufficiently strong magnetic field is provided.
In optical devices it is frequently necessary to rotate the polarization of an input optical beam. Rotating the polarization can be accomplished by the use of optically active materials, i.e. materials that exhibit different indices of refraction for circularly polarized beams in which the both the electric and magnetic vectors rotate in opposite senses. A plane polarized beam can be considered to be the vector sum of two circularly polarized beams of opposite sense, if the beams travel at different speeds because of the different indices of refraction then their relative phase changes and their sum is a plane polarized vector, which rotates about the axis of propagation. Thus, optically active materials can change the polarization direction of plane-polarized beams that travel through them when they have been exposed to a strong magnetic field. The amount by which a polarization is rotated depends on three factors: (1) the strength of the magnetic field; (2) the distance the beam travels in the material; and (3) an internal property of a material whose rotating strength is measured by the Verdet constant. The rotational angle is the product of these three factors, as in Equation 1.
Thus, after the optimal material has been selected, the desired degree of rotation can be attained either by a variation of path length or magnetic field. Since a longer path entails greater loss of beam energy due to absorption, a larger field source and an increased manufacturing expense of a longer optically active element, it is usually desirable to vary the strength of the magnetic field. Permanent magnets are much more suitable as magnetic field sources than electromagnets because the permanent magnet requires no electrical power and can be fabricated into a much more compact size. Therefore, permanent magnet structures that afford high magnetic fields with minimal bulk and weight that can also provide access to a light beam and accommodation of the optically active element are desirable for these purposes. Prior art arrangements have used a series of three cylindrical magnets placed together in tandem along a mutual axis with the two end magnets placed in magnetic opposition to the central magnet. FIG. 1 is an example of that prior art arrangement.
Referring now to FIG. 1, an axially magnetized cylindrical magnet structure 10 comprises cylindrical magnets 11–13 placed together in tandem along a longitudinal axis represented by broken line 14. The two end magnets 11 and 13 are placed in magnetic opposition to central magnet 12 and optically active elements 15 are positioned within the axial tunnel 16. The optically active elements 15 within the axial tunnel 16 are exposed to an input optical beam, indicated by arrow 17, which enters the axial tunnel 16. FIG. 1 also depicts representative dimensions. The axially magnetized cylindrical magnets 11–13 have magnetic poles situated on their circular end-surfaces with N poles 18 and S poles 19. The magnetic poles have an area density given by the expression:σ=M  (2)where M is the magnetization. It is these magnetic poles that according to Coulomb's inverse square law give rise to an axial field in the axially bored tunnel 16 through the central magnet 12. Mounting the end magnets 11 and 13 in tandem in opposition to central cylindrical magnet 12 has the effect of doubling the surface pole density on the end-surfaces 18 and 19 and hence the magnetic field in the tunnel 16. Because the fields in successive elements are in opposite directions, it is necessary for the respective materials in the successive elements to have opposing chiralities to result in the same sense of beam rotation. In the interiors of the outside end magnets 11 and 13, the magnetic field is increased by only about ⅓ since only their inner surfaces have effective double pole density. Also their outer ends detract from the magnetic field in the central magnet 12 because of their opposite charges. However, since the end magnets 11 and 13 are considerably more remote from the center magnet 12 than the inner surface, this detraction is small when compared to the addition provided by the inner surface. The magnetic fields in the outer end magnets 11 and 13 can also be used to further augment the total optical rotation by placing optically active elements of opposite chirality from that of central magnet 12 in the axial tunnel 16 to compensate for the reversed field direction there as compared to that in the tunnel 16 of the central magnet 12. The prior art tandem arrangement 10 provides a rotation induced by a potential difference between the end magnets 11 and 13 of 16 kilo-gilberts.
The prior art tandem arrangement suffers from a number of disadvantages, limitations and shortcomings based upon the cumbersome mass and bulk of the axially magnetized cylindrical magnet structure 10, as well as the need for a relatively lengthy structure to accommodate multiple optically active elements in the axial tunnel 16. Up until now, it has not been possible to provide the benefits of a Faraday rotator mechanism without suffering from the disadvantages, limitations and shortcomings of cumbersome mass and bulk, longer optically active elements and increasingly lengthy tunnels for the longer optically active elements. The present invention provides magnetic structures for Faraday rotators with significant decreases in mass, bulk and optically active element length, without suffering from the disadvantages, limitations and shortcomings of prior art structures. One embodiment of the Faraday rotator magnetic structure comprises a magic sphere augmented by an interior magnet that produces a similar magnetic potential difference, Bl, the shorter length, l, being compensated by a higher field, B. Another embodiment of the Faraday rotator magnetic structure comprises positioning two magic spheres in tandem to provide an advantageous significant reduction in mass.